Mixed finite elements and Newton-type linearizations for the solution of Richards' equation

✍ Scribed by Luca Bergamaschi; Mario Putti

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 264 KB
• Volume: 45
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/(sici)1097-0207(19990720)45:8<1025::aid-nme615>3.0.co;2-g

✦ Synopsis

We present the development of a two-dimensional Mixed-Hybrid Finite Element (MHFE) model for the solution of the non-linear equation of variably saturated ow in groundwater on unstructured triangular meshes. By this approach the Darcy velocity is approximated using lowest-order Raviart-Thomas (RT0) elements and is 'exactly' mass conserving. Hybridization is used to overcome the ill-conditioning of the mixed system. The scheme is globally ÿrst-order in space. Nevertheless, numerical results employing non-uniform meshes show second-order accuracy of the pressure head and normal uxes on speciÿc grid points. The non-linear systems of algebraic equations resulting from the MHFE discretization are solved using Picard or Newton iterations. Realistic sample tests show that the MHFE-Newton approach achieves fast convergence in many situations, in particular, when a good initial guess is provided by either the Picard scheme or relaxation techniques.